{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2009:KE67TUW3ZG4FXT25NQ5NBSSBZJ","short_pith_number":"pith:KE67TUW3","canonical_record":{"source":{"id":"0902.0801","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RA","submitted_at":"2009-02-04T21:41:47Z","cross_cats_sorted":["math.KT","math.RT"],"title_canon_sha256":"0a983cbcfc08403ae5b1d84e8955c6ba6190d58d48e3dc55e3143029f96fa3f1","abstract_canon_sha256":"bff4d26880bd4ad8b46e444142d1fefd64216f6a31576fcfc8b4b62b443cd8cf"},"schema_version":"1.0"},"canonical_sha256":"513df9d2dbc9b85bcf5d6c3ad0ca41ca7f6591b782bc208de0b8ce709334a688","source":{"kind":"arxiv","id":"0902.0801","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"0902.0801","created_at":"2026-05-18T02:58:10Z"},{"alias_kind":"arxiv_version","alias_value":"0902.0801v2","created_at":"2026-05-18T02:58:10Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.0902.0801","created_at":"2026-05-18T02:58:10Z"},{"alias_kind":"pith_short_12","alias_value":"KE67TUW3ZG4F","created_at":"2026-05-18T12:26:00Z"},{"alias_kind":"pith_short_16","alias_value":"KE67TUW3ZG4FXT25","created_at":"2026-05-18T12:26:00Z"},{"alias_kind":"pith_short_8","alias_value":"KE67TUW3","created_at":"2026-05-18T12:26:00Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2009:KE67TUW3ZG4FXT25NQ5NBSSBZJ","target":"record","payload":{"canonical_record":{"source":{"id":"0902.0801","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RA","submitted_at":"2009-02-04T21:41:47Z","cross_cats_sorted":["math.KT","math.RT"],"title_canon_sha256":"0a983cbcfc08403ae5b1d84e8955c6ba6190d58d48e3dc55e3143029f96fa3f1","abstract_canon_sha256":"bff4d26880bd4ad8b46e444142d1fefd64216f6a31576fcfc8b4b62b443cd8cf"},"schema_version":"1.0"},"canonical_sha256":"513df9d2dbc9b85bcf5d6c3ad0ca41ca7f6591b782bc208de0b8ce709334a688","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T02:58:10.746083Z","signature_b64":"Az7Xr2qL+cNiDp3JlN+PpsfAzUsHSlxiC+OpbhXpswxrEq5niWki6RR7fAYQqt2fp9NxHAWdFU9Sh3F9fJXYDw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"513df9d2dbc9b85bcf5d6c3ad0ca41ca7f6591b782bc208de0b8ce709334a688","last_reissued_at":"2026-05-18T02:58:10.745302Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T02:58:10.745302Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"0902.0801","source_version":2,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T02:58:10Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"2sOWqJefQTKM/z648gm9PIgwsRunptxGEBZVVBsuN1/jnxuhJvX1VBB9Rdn73S09pzQ9IWFt/NbRwdPSz+ivCA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-30T22:44:33.054778Z"},"content_sha256":"275f49ca2ddf30274260c8d5b5d72c682da2e3806915a1a7856440769d999be3","schema_version":"1.0","event_id":"sha256:275f49ca2ddf30274260c8d5b5d72c682da2e3806915a1a7856440769d999be3"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2009:KE67TUW3ZG4FXT25NQ5NBSSBZJ","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Cohomology of finite dimensional pointed Hopf algebras","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.KT","math.RT"],"primary_cat":"math.RA","authors_text":"J. Pevtsova, M. Mastnak, P. Schauenburg, S. Witherspoon","submitted_at":"2009-02-04T21:41:47Z","abstract_excerpt":"We prove finite generation of the cohomology ring of any finite dimensional pointed Hopf algebra, having abelian group of grouplike elements, under some mild restrictions on the group order. The proof uses the recent classification by Andruskiewitsch and Schneider of such Hopf algebras. Examples include all of Lusztig's small quantum groups, whose cohomology was first computed explicitly by Ginzburg and Kumar, as well as many new pointed Hopf algebras. We also show that in general the cohomology ring of a Hopf algebra in a braided category is braided commutative. As a consequence we obtain som"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"0902.0801","kind":"arxiv","version":2},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"references":{"count":0,"sample":[],"resolved_work":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","internal_anchors":0},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"},"verdict_id":null},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T02:58:10Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"wVa3zbWNJ+VvNjqXvbaD8FKn/V3Hkg8DSXRXs7/sWExZ2VbNkdQYQC1YP5FoialCQA+GYrHj31zkF5jKHd8DCA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-30T22:44:33.055116Z"},"content_sha256":"e093558a70873af84bd30127320d38195b846c4e555053bea486580175c7d0a7","schema_version":"1.0","event_id":"sha256:e093558a70873af84bd30127320d38195b846c4e555053bea486580175c7d0a7"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/KE67TUW3ZG4FXT25NQ5NBSSBZJ/bundle.json","state_url":"https://pith.science/pith/KE67TUW3ZG4FXT25NQ5NBSSBZJ/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/KE67TUW3ZG4FXT25NQ5NBSSBZJ/bundle.json","status":"primary"}],"public_keys":[{"key_id":"pith-v1-2026-05","algorithm":"ed25519","format":"raw","public_key_b64":"stVStoiQhXFxp4s2pdzPNoqVNBMojDU/fJ2db5S3CbM=","public_key_hex":"b2d552b68890857171a78b36a5dccf368a953413288c353f7c9d9d6f94b709b3","fingerprint_sha256_b32_first128bits":"RVFV5Z2OI2J3ZUO7ERDEBCYNKS","fingerprint_sha256_hex":"8d4b5ee74e4693bcd1df2446408b0d54","rotates_at":null,"url":"https://pith.science/pith-signing-key.json","notes":"Pith uses this Ed25519 key to sign canonical record SHA-256 digests. Verify with: ed25519_verify(public_key, message=canonical_sha256_bytes, signature=base64decode(signature_b64))."}],"merge_version":"pith-open-graph-merge-v1","built_at":"2026-06-30T22:44:33Z","links":{"resolver":"https://pith.science/pith/KE67TUW3ZG4FXT25NQ5NBSSBZJ","bundle":"https://pith.science/pith/KE67TUW3ZG4FXT25NQ5NBSSBZJ/bundle.json","state":"https://pith.science/pith/KE67TUW3ZG4FXT25NQ5NBSSBZJ/state.json","well_known_bundle":"https://pith.science/.well-known/pith/KE67TUW3ZG4FXT25NQ5NBSSBZJ/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2009:KE67TUW3ZG4FXT25NQ5NBSSBZJ","merge_version":"pith-open-graph-merge-v1","event_count":2,"valid_event_count":2,"invalid_event_count":0,"equivocation_count":0,"current":{"canonical_record":{"metadata":{"abstract_canon_sha256":"bff4d26880bd4ad8b46e444142d1fefd64216f6a31576fcfc8b4b62b443cd8cf","cross_cats_sorted":["math.KT","math.RT"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RA","submitted_at":"2009-02-04T21:41:47Z","title_canon_sha256":"0a983cbcfc08403ae5b1d84e8955c6ba6190d58d48e3dc55e3143029f96fa3f1"},"schema_version":"1.0","source":{"id":"0902.0801","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"0902.0801","created_at":"2026-05-18T02:58:10Z"},{"alias_kind":"arxiv_version","alias_value":"0902.0801v2","created_at":"2026-05-18T02:58:10Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.0902.0801","created_at":"2026-05-18T02:58:10Z"},{"alias_kind":"pith_short_12","alias_value":"KE67TUW3ZG4F","created_at":"2026-05-18T12:26:00Z"},{"alias_kind":"pith_short_16","alias_value":"KE67TUW3ZG4FXT25","created_at":"2026-05-18T12:26:00Z"},{"alias_kind":"pith_short_8","alias_value":"KE67TUW3","created_at":"2026-05-18T12:26:00Z"}],"graph_snapshots":[{"event_id":"sha256:e093558a70873af84bd30127320d38195b846c4e555053bea486580175c7d0a7","target":"graph","created_at":"2026-05-18T02:58:10Z","signer":{"key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signer_id":"pith.science","signer_type":"pith_registry"},"payload":{"graph_snapshot":{"author_claims":{"count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","strong_count":0},"builder_version":"pith-number-builder-2026-05-17-v1","claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"paper":{"abstract_excerpt":"We prove finite generation of the cohomology ring of any finite dimensional pointed Hopf algebra, having abelian group of grouplike elements, under some mild restrictions on the group order. The proof uses the recent classification by Andruskiewitsch and Schneider of such Hopf algebras. Examples include all of Lusztig's small quantum groups, whose cohomology was first computed explicitly by Ginzburg and Kumar, as well as many new pointed Hopf algebras. We also show that in general the cohomology ring of a Hopf algebra in a braided category is braided commutative. As a consequence we obtain som","authors_text":"J. Pevtsova, M. Mastnak, P. Schauenburg, S. Witherspoon","cross_cats":["math.KT","math.RT"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RA","submitted_at":"2009-02-04T21:41:47Z","title":"Cohomology of finite dimensional pointed Hopf algebras"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"0902.0801","kind":"arxiv","version":2},"verdict":{"created_at":null,"id":null,"model_set":{},"one_line_summary":"","pipeline_version":null,"pith_extraction_headline":"","strongest_claim":"","weakest_assumption":""}},"verdict_id":null}}],"author_attestations":[],"timestamp_anchors":[],"storage_attestations":[],"citation_signatures":[],"replication_records":[],"corrections":[],"mirror_hints":[],"record_created":{"event_id":"sha256:275f49ca2ddf30274260c8d5b5d72c682da2e3806915a1a7856440769d999be3","target":"record","created_at":"2026-05-18T02:58:10Z","signer":{"key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signer_id":"pith.science","signer_type":"pith_registry"},"payload":{"attestation_state":"computed","canonical_record":{"metadata":{"abstract_canon_sha256":"bff4d26880bd4ad8b46e444142d1fefd64216f6a31576fcfc8b4b62b443cd8cf","cross_cats_sorted":["math.KT","math.RT"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RA","submitted_at":"2009-02-04T21:41:47Z","title_canon_sha256":"0a983cbcfc08403ae5b1d84e8955c6ba6190d58d48e3dc55e3143029f96fa3f1"},"schema_version":"1.0","source":{"id":"0902.0801","kind":"arxiv","version":2}},"canonical_sha256":"513df9d2dbc9b85bcf5d6c3ad0ca41ca7f6591b782bc208de0b8ce709334a688","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"513df9d2dbc9b85bcf5d6c3ad0ca41ca7f6591b782bc208de0b8ce709334a688","first_computed_at":"2026-05-18T02:58:10.745302Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T02:58:10.745302Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"Az7Xr2qL+cNiDp3JlN+PpsfAzUsHSlxiC+OpbhXpswxrEq5niWki6RR7fAYQqt2fp9NxHAWdFU9Sh3F9fJXYDw==","signature_status":"signed_v1","signed_at":"2026-05-18T02:58:10.746083Z","signed_message":"canonical_sha256_bytes"},"source_id":"0902.0801","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:275f49ca2ddf30274260c8d5b5d72c682da2e3806915a1a7856440769d999be3","sha256:e093558a70873af84bd30127320d38195b846c4e555053bea486580175c7d0a7"],"state_sha256":"9f606fbb156b24996c31c3808fb85fef285032bf324fb3dbec438e3a6ac3641e"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"LpjdbTmCKD2CZTWgKdKKuvC52FgkkpuO0l0F9GUyPzD+FtiM7aK+TvVr57GbBxEiJY9Y9t87N/AGCsNjPGfACQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-30T22:44:33.057112Z","bundle_sha256":"9233a834593ca49999bcea89b8e9aa522c8ba8b6303a1b5a0d435ae94894f448"}}